Question

Suppose it takes 5 years for $20000 investment using continuous interest to doble

Answer 1

Given a continuous compound interest :

r is the interest rate per period and t is the number of periods = 5yrs

(1) A = amount, P = pricipal

`A=Pe^(rt)`
`\begin{gathered} (A)/(P)=e^(rt) \\ 2=e^(rt) \\ \ln 2=\ln e^(rt) \\ \ln e^(rt)=\ln 2 \\ rt=\ln 2 \\ r=(\ln 2)/(5) \end{gathered}`

(2) A(t) = Amount of money in the account after t years

`\begin{gathered} A(t)=20000 \\ A(t)=e^(rt) \\ 20000=e^(rt) \end{gathered}`